www.whyslopes.com
Volume 3, Why Slopes and More Math
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YOU are better than YOU think. Show yourself how:
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Logic
Mastery
Amazing, Amusing, Amorous, Delicious, Delightful, Edifying,
Strengthening Elixir.
It eases work & learning difficulties Makes the hard easier. Opens eyes.
Leads to greater precision.
in reading and
writing
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Caution: Site advice is approximately
correct, for some circumstances, not all. . That leaves room for thought and
refinement.. |
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Online Volume 2, Three Skills
for Algebra, Chapters 1 to 25 - skip 18., verbalizes and explains key skills
and concepts, those needed in calculus, again to make the hard easier. A visual
understanding of complex numbers
may serve as back ground info for partial fraction decomposition.
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A calculus course may ask for the computation of slope
mski = L by evaluating the limit directly. The rules and
properties of limits suggest how, at least in the simpler
cases. Then the course may introduce rules for
differentiation. (These rules for differentiation are
based on or justified by the rules and properties of
limits.)
- [Play
Video] 2 minutes: Product and Quotient
Rules for Differentiation. Statement Only
- [Play
Video] 2½ minutes: Product Rule for
Differentiation, indication of proof (why it
holds)
- [Play
Video] 3½ minutes: Three Notations for
derivatives, prime, functional or Liebniz y' = y'(x)
= dy/dx
- [Play
Video] 4¾ minutes: Why d/dx
(xn) = n xn-1 - Proof by mathematical
induction.
- [Play
Video] 4¾ minutes: Derivative of
Polynomials, Three Examples.
- [Play
Video] 4 minutes: Using the Quotient
Rule, Example with linear expression and quadratic
as numerator and denominator.
Differentiation rules say how to compute formulas
for f¢(x1) in a routine mechanical manner from formulas
for f(x), at least when the formula for f(x) is simple
enough. The proof, justification and further explanation
of rules for differentiation may be found in a calculus
course or book.
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For help in calculus, explore
Volumes
2. Three Skills
for Algebra
and 3. Why
Slopes & More Math, and Calculus
Introduction site area. See how to learn or teach key skills and
concepts, some not all.
Foreword, One Calculus preview and Online Chapters:
(V) signals video (RealPlayer Format) to
watch
Area Intro
Foreword
Chapter Descriptions
1. Introduction
Cal. Preview (1983 lesson why slopes)
2. Second Preview Begins
2 Skier in Motion (V)
2 The Skier (V)
2. Position Dependent (V)
3 Slope & Extrema (V)
4 Single Factor Analysis (V)
4 Two Factor (V)
4 More Factors (V)
4 With Divisors (V)
5 Maxima & Minima Tests
6 Jumps & Discontinuities
8 Review (optional)
9 On Calculus Studies
11 Slope of Slope
13 Acceleration
14 Limits & Error Control (V)
14 Limit of a Fn.
14. Limited Error Control
14 Signif. Digits
14 Cauchy Limits
14 Sequence Limits
14 Decimal Arith.
15 What is Slope (V)
15 Slope Calculation (V)
15 Slope, a Limit
15 Tangent Lines
15 Linear Approx.,
15 Limits via Algebra (V)
15 Recap.
PS.Chain Rule for Polys
PS Chain Rule- General (V) -
PS More Chain Rule (V)
PS - Sign Analysis (V)
16 What is Velocity
17 What is Area
18 Integration
18 Area Calculation
18 Fn DefN, 6 Ways
19 Logs & Powers
19 Natural Log.
19 Exponential Fn.
20 What's Next
21 Add Vectors
22 Complex #'s
23 Complex #'s
23 Trig Identity
23 Proofs of.
24 Complex Logs etc
Units in Calculations:
7 Velocity
7 Varying Velocity Example
7. Velocity Calculation
7 Changing Units
7 Same Velocity Motions
10 Slopes without Units.
10 Units & Slopes
10 Units in Cost vs. Quantity
10 How Units Appear
10 Unit Elimination
10 Partial Elimination
10 Interest & Units
12 More on Units
Content Guide
Enriched material: The Appendices of Volume
3 are located in the Real
Analysis Area.
Pigeon Hole Principle
Constant Difference Thm
Continuous Functions
Rational Functions
Mean Value Theorem
One Side Range Theorem
Range On One Side
Theorem
Integration
& Lipschitz
Continuity
These appendices continue the
decimal viewpoint of limits, error
control and continuity begun
in Chapter 14. The One Sided
Range Theorem is a postscript,
not in printed version.
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